I'm not sure if this is what you mean by "distribution", but I think Instagram won by being content-consumption-centric. People who used Flickr were mostly other photographers. People on Instagram are mostly your customers: people planning their own weddings, moms with newborn children, etc. It's basically a marketing platform, so it's a no-brainer for current or aspiring pros.
It sucks for passionate hobbyists, but photography is first and foremost an industry.
Also the friction of uploading a photo from iOS was (and pretty much still is, despite Instagram's best efforts to enshittify their app) much, much lower for Instagram.
If the Flickr app had had a "quick upload" flow like Instagram, they might have had a chance but (like almost everything Yahoo! did) they fumbled badly and wasted any potential they had.
It sucks for passionate hobbyists, but photography is first and foremost an industry.